Bandgap voltage references provide a stable voltage reference by summing voltages that have opposing temperature dependencies. For example, the voltage across a forward-biased PN junction will decrease approximately 2 milli-volts per degree Celsius as the temperature of the PN junction is increased. Such a temperature dependency may be denoted as a complementary-to-absolute-temperature (CTAT) dependency. In contrast, the difference in base-to-emitter voltages (ΔVBE) between matched transistors operating at different current densities shows a positive-to-absolute-temperature (PTAT) dependency that is proportional to the thermal voltage VT. The thermal voltage equals kT/q, where k is the Boltzmann constant, T is the absolute temperature in degrees Kelvin, and q is the magnitude of electronic charge. Thus, the thermal voltage will increase about 0.085 milli-volts per degree Celsius, giving it a PTAT temperature dependency. By proper scaling of the PTAT and CTAT voltages, a thermally stable voltage reference may be obtained.
A conventional bandgap reference 10 is shown in FIG. 1. Current source 20 generates a current I proportional to the thermal voltage. Thus, because current I increases with temperature, passing current I through a resistor of resistance R will generate a PTAT voltage equaling I*R. A diode D, which may comprise a diode-connected transistor, is in series with resistor R and is forward biased in response to current I to provide a CTAT voltage VBE. Taking the output voltage Vout from node A provides the sum of the CTAT and PTAT voltages. By choosing the value of R appropriately, Vout will be thermally stable. In other words, Vout may be made independent with respect to changes in temperature.
Although bandgap reference 10 may provide a thermally stable output voltage assuming a careful choice for resistance R, the reality is typically that some thermal variations will be observed in a certain percentage of devices during mass production. For example, the PTAT voltage depends upon the matching between two transistors, which may vary during production due to transistor dimension and doping variations. In addition, thermal variation may result from modeling inaccuracies. As a result, trimmable bandgap voltage references have been developed that include variable resistances. Through means such as switches, the resistances are varied to compensate for process inaccuracies so as to balance the PTAT and CTAT voltages. Although trimmable bandgap voltage references allow process inaccuracies to be addressed, these references often require an excessive number of adjustments and still suffer from mismatches.
Accordingly, there is a need in the art for improved trimmable bandgap voltage references that can provide an output voltage that is stable with respect to temperature changes without requiring an excessive number of adjustments or switches.